Properties

Label 5070.2.b
Level $5070$
Weight $2$
Character orbit 5070.b
Rep. character $\chi_{5070}(1351,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $27$
Sturm bound $2184$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5070.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(2184\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5070, [\chi])\).

Total New Old
Modular forms 1148 100 1048
Cusp forms 1036 100 936
Eisenstein series 112 0 112

Trace form

\( 100q + 4q^{3} - 100q^{4} + 100q^{9} + O(q^{10}) \) \( 100q + 4q^{3} - 100q^{4} + 100q^{9} - 4q^{10} - 4q^{12} - 8q^{14} + 100q^{16} - 8q^{22} - 100q^{25} + 4q^{27} - 16q^{29} - 4q^{30} - 8q^{35} - 100q^{36} + 32q^{38} + 4q^{40} + 8q^{42} - 16q^{43} + 4q^{48} - 52q^{49} - 8q^{55} + 8q^{56} - 40q^{61} + 16q^{62} - 100q^{64} - 8q^{66} + 16q^{69} - 8q^{74} - 4q^{75} + 80q^{77} - 16q^{79} + 100q^{81} - 16q^{87} + 8q^{88} - 4q^{90} - 32q^{94} - 32q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5070, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5070.2.b.a \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots\)
5070.2.b.b \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots\)
5070.2.b.c \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
5070.2.b.d \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
5070.2.b.e \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.f \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.g \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.h \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.i \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots\)
5070.2.b.j \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.k \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+4iq^{7}+\cdots\)
5070.2.b.l \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+5iq^{7}+\cdots\)
5070.2.b.m \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.n \(2\) \(40.484\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+2iq^{7}+\cdots\)
5070.2.b.o \(4\) \(40.484\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}-\zeta_{12}q^{6}+\cdots\)
5070.2.b.p \(4\) \(40.484\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}q^{6}+\cdots\)
5070.2.b.q \(4\) \(40.484\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+q^{3}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}q^{6}+\cdots\)
5070.2.b.r \(4\) \(40.484\) \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
5070.2.b.s \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.t \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.u \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.v \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.w \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{5}q^{2}+q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.x \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) \(q-\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.y \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.z \(6\) \(40.484\) 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.ba \(8\) \(40.484\) 8.0.\(\cdots\).1 None \(0\) \(8\) \(0\) \(0\) \(q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5070, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2535, [\chi])\)\(^{\oplus 2}\)